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- W2891631191 abstract "Let $A_{1},...A_{m}$ be a $ntimes n$ invertible matrices. Let $0 leq alpha<n$ and $0<alpha_{i}<n$ such that $alpha_1 + ... + alpha_m = n- alpha$. We define% begin{equation*} T_{alpha}f(x)=int frac{1}{leftvert x-A_{1}yrightvert ^{alpha _{1}}...leftvert x-A_{m}yrightvert ^{alpha _{m}}}f(y)dy. end{equation*}% In cite{U-V} we obtained the boundedness of this operator from $L^{p(.)}(% mathbb{R}^{n})$ into $L^{q(.)}(mathbb{R}^{n})$ for $frac{1}{q(.)}=frac{1% }{p(.)}-frac{alpha }{n},$ in the case that $A_{i}$ is a power of certain fixed matrix $A~ $and for exponent functions $p$ satisfying log-Holder conditions and $p(Ay)=p(y),$ $yin mathbb{R}^{n}$ $.$ We will show now that the hypothesis on $p$, in certain cases, is necessary for the boundedness of $T_{alpha}$ and we also prove the result for more general matrices $A_{i}.$ footnote{Partially supported by CONICET and SECYTUNC} footnote{Math. subject classification: 42B25, 42B35.} footnote{Key words: Variable Exponents, Fractional Integrals.}" @default.
- W2891631191 created "2018-09-27" @default.
- W2891631191 creator A5066532566 @default.
- W2891631191 date "2018-09-04" @default.
- W2891631191 modified "2023-09-27" @default.
- W2891631191 title "A generalization of the boundedness of certain integral operators in variable Lebesgue spaces" @default.
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